Spain's Economy Minister Luis de Guindos (l) talks with International Monetary Fund (IMF) Managing Director Christine Lagarde at a Eurogroup meeting in Brussels on Monday. The eurozone's finance ministers and the IMF are currently engaged in an unusually public debate over how to deal with Greece's debt crisis, as the country faces a financial deadline on Friday.

In a rare display of disagreement, eurozone finance ministers today clashed with IMF chief Christine Lagarde over the way to prevent crisis-stricken Greece from collapsing completely from its public debts.

The eurozone has come to the conclusion that the target to have Greece lower its debt-to-GDP ratio to 120 percent by 2020 is too ambitious. A 120 percent ratio is widely perceived as the threshold above which an economy cannot operate any longer – and Greece’s debt to GDP ratio is expected to hit 190 percent next year. So eurozone finance ministers decided to give Greece two extra years to reach 120 percent.

“The target, as far as the time-frame is concerned, has been postponed to 2022,” said eurozone chief Jean-Claude Juncker. Of course this would mean two more years that Greece would depend on financial aid.

But the announcement visibly upset Ms. Lagarde. She and the IMF insist that the existing aim of Greece reaching the 120 percent threshold by 2020 should remain, and that in order to help Athens, the eurozone governments should write off some of Greece’s debt. Such a haircut – a debt write-off – was agreed to by Greece’s private lenders at the beginning of the year, shaving more than €100 billion off the country’s obligations.

But with an economy shrinking at the rate of more than 5 percent and wide parts of the population deeply opposed to the austerity measures imposed in return for international aid, Greece may still not be able to get back on its feet.

So now the IMF is asking public lenders, namely the ECB, to write off Greek debt. But this would affect taxpayers in the whole eurozone, most of all its biggest economy, Germany. And the German government, up for election in just under a year, will have none of it.

"There's a debate about a haircut for official creditors. On that I will say, and most countries have said so in the past few weeks, that that's legally not possible," said German finance minister Wolfgang Schäuble in Brussels.

The unusually public debate between the IMF and Europe comes as Greece faces a looming bond purchase for which it is struggling to raise the money. Despite billions of international financial aid and sweeping cuts in public spending, Greece has been unable to escape the downward spiral of sovereign debt and a shrinking economy. And this Friday, the government in Athens is obligated to buy back bonds worth €5 billion ($6.35 billion).

Greece had hoped to receive a tranche this week of €31 billion ($39 billion) out of the second bailout package agreed by the troika over a year ago. But that hope was shattered when eurozone finance ministers meeting in Brussels postponed a decision on the payment until next week, citing the need to further assess Greece’s ability to pay back its debts in the foreseeable future.

The clash among the troika members is bound to make financial markets around the globe nervous again. Investors will likely wonder how serious German Chancellor Angela Merkel was when, during her recent trip to Athens, she stressed that to keep Greece within the common currency was her main priority.